“I’m closer to a daydreamer by nature, and for me mathematical research is a repetition of dreaming and waking up.”
beautiful!
The volume has to be greater than 1 unit in order to be a solution so it could be harder in higher dimensions.
1. If the walls are vertical and you are maximizing the horizontal area of the sofa and you are not allowed to reorient the sofa, then the problem collapses to the 2D case and the solution is the same.
2. If you are allowed to reorient the sofa while moving it, and the sofa doesn't have a minimum height, and the ceiling is arbitrarily high, then the sofa can be arbitrarily large by angling it to an arbitrary degree and then setting it flat for measuring.
3. So the in between case is where the ceiling is of some limited height and/or the sofa is of some arbitrary height, and then you have to decide whether the sofa has to be an extrusion of a 2D shape, or if it can be an arbitrary shape, at which point you're maximizing volume rather than area. And for that the obvious lower bound is the 2D maximum shape * the ceiling height. But maybe there's better?
Given a rectangle tunnel, twist it so the walls become the ceiling, and also turn it in the same time. Seems like the same problem..
What is solved here is maximum shape, it feels like moving a object like this in 3D is basically a robot planning thing which in it self obviously magic for me. Finding a continuous path in a configuration space is the easy part, but then you have to understand how that changes when your shape changes.
You could make the 3D case more interesting by having two corners: one in the plane and one out of the plane. It seems to me that that would need a new solution.
To make 3D relevant for a single turn, one of the hallways could be rotated 45° lengthwise.
https://colab.research.google.com/github/google-deepmind/alp...
The problem asks for the largest 2D shape that can be slid around a right-angle corner in a unit-width hallway.
Here is the perfect fitting sofa: https://en.wikipedia.org/wiki/File:Gerver.svg
That's especially easy to imagine with tables, but sofas also count.
There are also sofas that can be easily taken apart. Eg one of our sofas at home, an L-shaped sofa, comes apart into two pieces.
I would contend that it's still useful since you'd be able to turn the corner without over-complicating it by getting it into some weird tilt position.
That might give you a feasible solution, but I doubt it's optimal.
Though I guess writing like this doesn't pay off in the modern world. Most readers don't consistently pay attention when reading, and to be honest, I don't either.
i.e. if you apply the zeta function to a complex number, and you get zero, then that number must have been either a negative even integer or had a half as its real part.
What could be simpler than that? Those are all fairly simple concepts, and the definition of the function itself is nothing too exotic. I think any highschooler should be able to understand the statement and compute some values of zeta numerically. I'd like to see a statement about couches written so succinctly with only well-defined terms!
(I'm being intentionally a bit silly, but part of the magic of the Riemann Hypothesis is that it's relatively easy to understand its statement, it's the search for a proof that's astonishingly deep.)
As penance I did go an have a look for suitable numerical techniques for calculating zeta with Re(s)<1 and there are some, e.g. https://people.maths.bris.ac.uk/~fo19175/talks/slides/PGS_ta...
At risk of being tongue-in-cheek, a monad is just a monoid in the category of endofunctors, what's the problem?
I agree with you that Quanta doesn't always "allow specialists to understand exactly what's being claimed", which is a problem; but linking to the research papers greatly mitigates that sin.
[1] https://www.quantamagazine.org/the-largest-sofa-you-can-move...
And here's how they clearly explain the proof strategy.
> First, he showed that for any sofa in his space, the output of Q would be at least as big as the sofa’s area. It essentially measured the area of a shape that contained the sofa. That meant that if Baek could find the maximum value of Q, it would give him a good upper bound on the area of the optimal sofa.
> This alone wasn’t enough to resolve the moving sofa problem. But Baek also defined Q so that for Gerver’s sofa, the function didn’t just give an upper bound. Its output was exactly equal to the sofa’s area. Baek therefore just had to prove that Q hit its maximum value when its input was Gerver’s sofa. That would mean that Gerver’s sofa had the biggest area of all the potential sofas, making it the solution to the moving sofa problem.
Edit: This article from September has a bit more: https://www.popsci.com/science/gervers-sofa-problem-solved/
So I don’t think this article can even qualify as a good example for explaining math problems to laymen.
Here's a silly one: since 1, 3, 5 and 7 are primes, it almost seems obvious that all odd numbers are prime. Naturally, they are not, and there are countless proofs about various prime number generators to show that they can generate prime numbers, which are really prime.
[1] https://mathenchant.wordpress.com/2025/04/21/is-1-prime-and-...
The "intuitive" argument that 1 is prime is that, as with prime numbers, you can't produce it by multiplying some other numbers. That's true!
But where the primes are numbers that are the product of just one factor, 1 is the product of zero factors, a very different status. The argument over whether 1 should be called a "prime number" is almost exactly analogous to the argument over whether 0 should be called a positive integer.†
It's more broadly analogous to the argument over whether 0 should be called a "number", but that argument was resolved differently. "Number" was redefined to include negatives, making 0 a more natural inclusion. If you similarly redefine "prime number" to include non-integral fractions (how?), it might make more sense to consider 1 to be one.
† Note that there is no Fundamental Theorem of Addition stating that the division of a sum into addends is unique. It isn't, but 0 is the empty sum anyway.
What do you mean?
The factors of 3 are 3 and 1. The factors of 1 are 1?
3 is the product of the members of {3}.
1 is the product of the members of the empty set.
We’re excluding the unit when defining these factor sets (ie, multiplicative identity) because it removes unique factorization.
That 1 is the unit is also why it’s the value for the product of the empty set because we want the product of a union of sets to match the product of a product of sets. But we don’t exclude it from the primes for that reason.
Oh! So it’s like Python’s `reduce(multiply,s,initial=1)`, such that s={} still gets you 1. Alright, that makes sense.
This seems to be circular since it assumes that 1 is not prime
For a long time, it was thought this might be the optimal shape, but it was never proven. And it couldn't have been because it turns out that you can do better: the Gerver sofa (1992) is a more complicated shape, composed of 18 curve segments and has A=2.2195.
Nobody knew whether there might be an even better shape until now (assuming the proof holds up).
https://en.wikipedia.org/wiki/File:Gerver%E2%80%99s_and_Hamm...
This was also the problem in Dirk Gently’s Holistic Detective Agency, so fictionally this problem had already been solved.
https://en.wikipedia.org/wiki/Dirk_Gently%27s_Holistic_Detec...
https://en.wikipedia.org/wiki/The_Long_Dark_Tea-Time_of_the_...
In the novels, a stuck sofa is revealed to have got there because a retired Time Lord, Professor Urban Chronotis, briefly materialised his TARDIS in such a place it provided a doorway. So the books are extremely loosely tied into the Dr Who universe.
Don't let this put you off.
"The atmosphere is poisonous. I'm not sure what's in it but it would certainly get your carpets nice and clean."
https://centers.ibs.re.kr/html/living_en/housing/moving2.htm...
https://koreajoongangdaily.joins.com/news/2024-05-18/culture...
It's a bit like finding the fastest way possible to beat Super Mario Bros 3 while collecting the minimum number of coins. A solution to a neat puzzle, but it doesn't carry the epistemic weight of finding out how the universe works, even if both pieces of knowledge are equally useless.
1: And of course this point doesn't apply to applied math.
gnabgib•1mo ago
Discussion on the paper (131 points, 2024, 36 comments) https://news.ycombinator.com/item?id=42300382
svat•1mo ago
The mention of "Scientific American" in this article refers to something more recent:
> US magazine Scientific American named the research by Baek Jin-eon among its top 10 mathematical breakthroughs of 2025
This is a reference presumably to https://www.scientificamerican.com/article/the-top-10-math-d... "The 10 Biggest Math Breakthroughs of 2025" (dated December 19, 2025). It's more recent than your link https://www.scientificamerican.com/article/mathematicians-so... "Mathematicians Solve Infamous ‘Moving Sofa Problem’" (dated February 4, 2025).
November 2024 is when he posted the preprint on the arXiv: https://arxiv.org/abs/2411.19826 "Optimality of Gerver's Sofa" (submitted on 29 Nov 2024).
There has been other reporting since then, such as in Quanta Magazine: https://www.quantamagazine.org/the-largest-sofa-you-can-move... "The Largest Sofa You Can Move Around a Corner" (dated February 14, 2025). (Contains quotes from his adviser Michael Zieve, and from Gerver himself.)
The paper is still under review at the Annals of Mathematics, so there will be likely be another round of reporting when it has finished peer review and is published.